Carleton College

Complex Systems as Evolutionary Systems

Lynn S. Fichter, Department of Geology and Environmental Science, James Madison University

March 25, 2010

Ask the average person, "What is the theory of evolution?" and you are likely to get answers like "natural selection", or "survival of the fittest", or "Darwin's theory." Because these ideas are systematically taught in classrooms, they may represent the only evolutionary theory people know. But, ask, "What is the theory of Earth evolution?" you will likely get a blank stare, or at best a superficial discussion of the fossil record. All systems that evolve, including mineral and rock systems, atmospheric systems, ecosystems, economic systems, social systems, etc. are complex systems in the technical sense of that term. Conversely, biological evolution is a complex system, but, until recently has not been thought of or modeled as a complex system. My work over the past decade has been to develop a coherent framework, strategy and rubrics for teaching chaos/complex systems as evolutionary systems and applying them to a wide diversity of systems.

There are impediments to incorporating chaos and complex evolutionary systems ideas into traditional scientific disciplines and into the classroom. One impediment is the dominance of linear/equilibrium thinking and training in our schools. Teaching chaos/complex systems principles requires students be familiar with mathematical principles, techniques, and properties not yet systematically taught. A second impediment is the inconsistent and ambiguous use of the terms "complex" and "system." A third impediment is the domination of biological evolutionary theory as the only systematic mechanism for evolutionary change. A fourth impediment is the absence of rubrics for introducing chaos/complex systems theories and modeling techniques in class rooms.

To say a system is complex is not the same as saying it is a complex system. A complex system, in the technical sense, is a group of "agents" (individual interacting units, like birds in a flock, sand grains in a ripple, or individual units of friction along a fault zone), existing far from equilibrium, interacting through positive and negative feedbacks, forming interdependent, dynamic, evolutionary networks, that possess universality properties common to all complex systems: bifurcations, evolution to sensitive dependent critical states, avalanches of changes following power law distributions, with fractal organization, and dynamic behavior as strange attractors that often exhibit bi-stable behavior.

Chaos/complex systems theory behaviors are explicit, with their own assumptions, approaches, cognitive tools, and models that must be taught as deliberately and systematically as the equilibrium principles normally taught to students, or the progressions from pre-algebra, to algebra, to calculus. We have developed a learning progression of concept building from basic principles of chaos theory, through a variety of complex systems, and ending with examples of how such systems work in the real world.

Complex systems are usually defined as self-organizing systems; Chris Lucas, for example, (http://www.calresco.org/lucas/cas.htm) states "complexity theory states that critically interacting components self-organize to form potentially evolving structures exhibiting a hierarchy of emergent system properties." Self-organization is, however, not the only way that complex systems evolve. We need a more comprehensive framework that can put all systems on an integrated, universal evolutionary theoretical foundation.

If we define evolutionary change as any process that leads to increases in complexity, diversity, order, and/or interconnectedness then there are at least three distinct mechanisms, or theories of evolution: elaboration, self-organization, and fractionation.

Elaborating evolution (subsuming biological evolution as a special case) begins with a seed, an ancestor, or a randomly generated population of agents, and evolves by generating, and randomly mutating, a large diversity of descendants which are evaluated by an external fitness function; those that do not measure up are selected out. The fitness function may be a real environment, an abstract environment, or another "species" of agents. What is common to all elaborating evolutionary systems is the General Evolutionary Algorithm (Beinhocker, 2007): 1) Differentiate, 2) Select, 3) Amplify. Any system that evolves by this process, regardless of the actual units that are differentiating and being selected, is an elaborating evolutionary system. For example, these algorithms are commonly used in computing to find exact or approximate solutions to optimization and search problems. In systems terminology differentiate equals positive feedback (an increase in the amount and diversity of information), while (natural) selection is negative feedback (trimming back of information).

Self-organizing evolution begins with an initial state of random agents that through the application of simple rules of interaction among the agents (e.g. an algorithm, or chemical/physical laws) evolves a system of ordered structures, patterns, and/or connections without control or guidance by an external agent or process; that is, pulls itself up by its own boot straps. A wide diversity of specific mechanisms have been identified for self organization, including: self-organized criticality, boids, cellular automata, autocatalytic networks, network theory, and oscillating chemical reactions, but they all come down to "Local Rules leads to Global Behavior."

Fractionating evolution begins with a complex parent which is physically, chemically, or biologically divided into fractions—through the addition of the right amount of energy—because of differences in the size, weight, valence, reactivity, etc. of the component particles. Fractionation as a process is pervasive in natural systems (rock and atmospheric evolution, biochemistry, etc.) and is a widespread and well understood industrial process (e.g. fractionation of petroleum, and purification of almost any thing you can imagine.) Scientists and engineers have developed analytical and sophisticated models for these systems. Fractionation is not a mystery. On the other hand, we are unaware of any computer based experimental programs that explore principles of fractionating evolution, either in the spirit of the General Evolutionary Algorithm for elaborating evolution, or comparable to the many specific self-organizing evolutionary algorithms. There are challenges, benefits, and opportunities for exploring these elaborating, self-organizing, and fractionating complex evolutionary systems. There are decades of work in every realm of the sciences to build a theoretical evolutionary foundation based on chaos/complex systems theories to our disciplines, and this should please and challenge us as scientists and teachers.

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